Temperature phase diagrams, construction

The phase diagram constructed in this way, with the assumption that the difference in free energy of liquid lead and solid lead, Fo(l) — Fg(c), is a linear function of the temperature, and that the other parameters remain unchanged, is shown as Fig. 8. It is seen that it is qualitatively similar to the phase diagram for the lead-thallium system in the range 0-75 atomic percent thallium. 

Only for U, Np and Pu sufficient experimental work was carried out so that a pressure-temperature phase diagram can be constructed. 

We calculate the free energies of phases of chemical reaction (1) for the following investigation and comparison at different temperatures for the purpose of phase diagram construction. 

An analysis of the curves of concentration and temperature dependences of free energies provides a possibility of phase diagram construction and this diagram defines the concentration and temperature regions of all phases realization. The phase diagram corresponds to experimental data of manifestation of phases of chemical reaction (1) in the course of temperature rise. 

The temperature-composition phase diagram constructed from thermal arrests observed in the MoFe-UFa system is characteristic of a binary system forming solid solutions, a minimum-melting mixture (22 mole % UFe at 13.7°C.), and a solid-miscibility gap. The maximum solid solubility of MoFq in the UFe lattice is about 30 mole % MoFe, whereas the maximum solid solubility of UFe in the MoFe lattice is 12 to 18 mole % UFe- The temperature of the solid-state transformation of MoFe increases from ——lO C. in pure MoFe to 5°C. in mixtures with UFe, indicating that the solid solubility of UFe is greater in the low temperature form of MoFe than in the high temperature form of MoFe- This solid-solubility relationship is consistent with the crystal structures of the pure components The low temperature form of MoFe has an orthorhombic structure similar to that of UFe. 

Before carrying out kinetic measurements it is imperative that the equilibrium properties of the system under study be known. This information is most conveniently presented in the form of temperature-composition (T-C) phase diagrams. Two new approaches, utilizing TRXRD, which expedite T-C phase diagram construction have been developed and are reviewed in Sect. 3. 

Two mesophases may coexist over small ranges of composition and temperature. Phase diagrams have been constructed for a large number of binary systems. Transitions may be brought about from any one of the mesophases directly to the isotropic solution at appropriate temperatures. Ternary and higher-component systems exhibit essentially the same types of structures, the phase diagrams being of course much more complicated. 

Figure 4.5 Phase diagram constructed from the data of Fig. 4.4 showing the binodal (B) and spinodal (S) curves. The upper critical solution temperature (UCST) is shown.

The case of block copolymers is peculiar and deserves a specific development. In such a structure, the A and B blocks are connected to one another by a covalent bond, and their respective molar mass and composition can be varied independently. Being incompatible, A and B blocks tend to minimize their surface of contact but, contrary to the mere blends of two polymers they cannot phase separate to a macroscopic scale due to the bond which links them. Classical composition-temperature phase diagrams cannot be constructed for block copolymers as for the corresponding blends. Indeed the A and B blocks are forced to self-organize in domains of more reduced nano- or mesoscopic size. The transition from a homogeneous blend to a system composed of ordered phases as well as the size and the morphology of these ordered phases depend on two elements the product Xab " (X = total degree of polymerization) and the dissymmetry in size of the two blocks. 

Equilibrium phase diagram constructed for the PEO -Znl2 polymeric system. The transition temperatures were observed by DTA= DSC ° . 

Phase diagrams are constructed by measuring the temperatures and pressures at which phase changes occur. Approximate phase diagrams such as those shown in Figures 11-39 and 11-40 can be constmcted from the triple point, normal melting point, and normal boiling point of a substance. Example illustrates this procedure. 

A phase diagram of the symmetric PS-fc-PI blended with PS homopolymer of shorter chain lengths was constructed by Bodycomb et al. [ 174]. The effect of blend composition on the ODT is shown in Fig. 56 along with the results of mean-field calculations. In analogy to MFT the addition of homopolymer decreases the ODT temperature for the nearly symmetric diblock copolymer. 

Analyzing theoretically the thermodynamic behavior of the melt of a proteinlike copolymer, authors of work [39] did not confine themselves to the construction of its phase diagram. They also calculated the temperature dependencies of amplitudes and periods of mesophases, as well as their volume fractions in two-phase regions on these diagrams. This permitted them to reveal some important distinctions in the thermodynamic behavior of melts of Markovian and proteinlike heteropolymers. 

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